Description: This is the final version of the article. It first appeared from the World Scientific Publishing Company via http://dx.doi.org/10.1142/S0218271816410133

Abstract: We present in detail the Einstein equations in the Baumgarte–Shapiro–Shibata–Nakamura formulation for the case of D-dimensional spacetimes with SO(D−d)isometry based on a method originally introduced in Ref. 1. Regularized expressions are given for a numerical implementation of this method on a vertex centered grid including the origin of the quasi-radial coordinate that covers the extra dimensions with rotational symmetry. Axisymmetry, corresponding to the value d = D − 2, represents a special case with fewer constraints on the vanishing of tensor components and is conveniently implemented in a variation of the general method. The robustness of the scheme is demonstrated for the case of a black-hole head-on collision in D = 7 spacetime dimensions with SO(4) symmetry.

Keywords: black holes, numerical relativity, higher dimensions

Sponsorship: U.S. is supported by the H2020 ERC Consolidator Grant “Matter and strong-field gravity: New frontiers in Einstein’s theory” grant agreement No. MaGRaTh–646597, the H2020-MSCA-RISE-2015 Grant No. StronGrHEP-690904, the STFC Consolidator Grant No. ST/L000636/1, the SDSC Comet and TACC Stampede clusters through NSF-XSEDE Award Nos. PHY-090003, the Cambridge High Performance Computing Service Supercomputer Darwin using Strategic Research Infrastructure Funding from the HEFCE and the STFC, and DiRAC’s Cosmos Shared Memory system through BIS Grant No. ST/J005673/1 and STFC Grant Nos. ST/H008586/1, ST/K00333X/1. P.F. and S.T. are supported by the H2020 ERC Starting Grant “New frontiers in numerical general relativity” grant agreement No. NewNGR- 639022. P.F. is also supported by a Royal Society University Research Fellowship. W.G.C. and M.K. are supported by STFC studentships.